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Simplifying 2x2 + -268x + 5672 = 0 Reorder the terms: 5672 + -268x + 2x2 = 0 Solving 5672 + -268x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2836 + -134x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2836 + -134x + x2)' equal to zero and attempt to solve: Simplifying 2836 + -134x + x2 = 0 Solving 2836 + -134x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2836' to each side of the equation. 2836 + -134x + -2836 + x2 = 0 + -2836 Reorder the terms: 2836 + -2836 + -134x + x2 = 0 + -2836 Combine like terms: 2836 + -2836 = 0 0 + -134x + x2 = 0 + -2836 -134x + x2 = 0 + -2836 Combine like terms: 0 + -2836 = -2836 -134x + x2 = -2836 The x term is -134x. Take half its coefficient (-67). Square it (4489) and add it to both sides. Add '4489' to each side of the equation. -134x + 4489 + x2 = -2836 + 4489 Reorder the terms: 4489 + -134x + x2 = -2836 + 4489 Combine like terms: -2836 + 4489 = 1653 4489 + -134x + x2 = 1653 Factor a perfect square on the left side: (x + -67)(x + -67) = 1653 Calculate the square root of the right side: 40.657102701 Break this problem into two subproblems by setting (x + -67) equal to 40.657102701 and -40.657102701.Subproblem 1
x + -67 = 40.657102701 Simplifying x + -67 = 40.657102701 Reorder the terms: -67 + x = 40.657102701 Solving -67 + x = 40.657102701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + x = 40.657102701 + 67 Combine like terms: -67 + 67 = 0 0 + x = 40.657102701 + 67 x = 40.657102701 + 67 Combine like terms: 40.657102701 + 67 = 107.657102701 x = 107.657102701 Simplifying x = 107.657102701Subproblem 2
x + -67 = -40.657102701 Simplifying x + -67 = -40.657102701 Reorder the terms: -67 + x = -40.657102701 Solving -67 + x = -40.657102701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + x = -40.657102701 + 67 Combine like terms: -67 + 67 = 0 0 + x = -40.657102701 + 67 x = -40.657102701 + 67 Combine like terms: -40.657102701 + 67 = 26.342897299 x = 26.342897299 Simplifying x = 26.342897299Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.657102701, 26.342897299}Solution
x = {107.657102701, 26.342897299}
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